Simulating quantum systems to model their dynamics and energy spectra is one of the most promising applications of digital quantum computers. Indeed, the difficulty of performing such simulations on classical computers led Feynman [1]} and others to propose the idea of quantum computation. In 1996, Lloyd proposed the first explicit quantum algorithm for simulating local Hamiltonians [2]}. Since then, various quantum simulation algorithms have been developed [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, with potential applications in studying condensed matter physics [15]}, quantum chemistry [16]}, [17]}, quantum field theories [18]}, [19]}, superstring/M-theory [20]}, as well as in designing other classical [21]} and quantum algorithms [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}.
